When observing an object under a microscope, it is often preferable to have simultaneous high image resolution together with a large depth of field. An example is a surgical microscope where surgeons need sharp resolution of an affected tissue point image but also need a large depth of field to provide orientation and context. However, for a fixed optical system these parameters are not independent and are fundamentally related through the numerical aperture (NA) of the optical system. For example, approximate formulas for each of depth of field (DOF) and a smallest feature that can be resolved (RES) for an optical system are: DOF=λ/NA2; and RES=0.61 λ/NA (where λ is the average wavelength of illumination light, RES indicates a smallest feature that can be resolved. Hence as NA decreases in order to increase a resolution of an optical system (e.g. decrease the RES value), the DOF increases. Hence it is clear that increasing resolution is achieved at the expense of decreasing depth of field, and vice versa. In particular, since DOF depends inversely on square of NA, an increase in resolution (e.g. a decrease in RES) is very taxing on the DOF.
In conventional optical systems, the NA of a microscope typically retains the same size during a single image or video acquisition which means that a decision about the trade-off between high resolution (e.g. reducing RES) and large depth of field (e.g. increase DOF) has to be made before each image or video sequence acquisition. It is possible to acquire an image/video with high resolution with small depth of field or vice versa but not is not possible to achieve both simultaneously.